[R] GLM with Binomial Distribution

Leif Rasmuson rasmuson at uoregon.edu
Tue Jul 23 20:53:16 CEST 2013

Hi All,

I am working on re-analyzing per a reviewers request.

The goal of the project was to determine if the presence of predatory 
fishes caused female crabs to delay the release of larvae. Number of 
releases were recorded at three time periods: 1 hour before the 
simulated tide, 3 hours after the simulated tide and 6 hours after the 
tide. Predators were introduced at high tide and removed just following 
the 3 hour observation. Thus we have two categorical variables with 
three levels each. Time: pre-introduction, after introduction and after 
removal. Predator: no-predator, predator of adults and predator of larvae.

The number of females was not consistent between trials so my initial 
method was to use the SRH extension of the Kruskal wallace test to 
examine the percent of of larvae released.

A reviewer suggested that I use a GLM with a binomial distribution and 
logit link to analyze the larval release patterns. I used Crawley's book 
to analyze the data based on proportions. See code below. The problem I 
am running into is that the model is not including the predator control 
and interaction is excluding the predator control and the introduction 
time periods. Is this just the nature of using a binomial distribution 
(and/or our small sample size) or is there a way to force R to include 
all the factors and run all the interactions?


rv <-cbind(y,N)

 > model1=glm(y~GLM$Time*GLM$Treatment-1,family=binomial)
 > summary(model1)

glm(formula = y ~ GLM$Time * GLM$Treatment - 1, family = binomial)

Deviance Residuals:
Min 1Q Median 3Q Max
-1.6024 -0.7146 -0.4284 -0.2512 3.9885

Estimate Std. Error z value Pr(>|z|)
GLM$TimeAfterIntroduction -1.8289 0.2297 -7.963 1.68e-15 ***
GLM$TimeAfterRemoval -3.6571 0.5064 -7.222 5.14e-13 ***
GLM$TimePreIntro -5.0626 1.0029 -5.048 4.46e-07 ***
GLM$TreatmentPlanktivore -0.0123 0.3211 -0.038 0.969
GLM$TreatmentPredator -0.1589 0.3311 -0.480 0.631
GLM$TimeAfterRemoval:GLM$TreatmentPlanktivore 0.5339 0.7132 0.749 0.454
GLM$TimePreIntro:GLM$TreatmentPlanktivore 0.6561 1.2708 0.516 0.606
GLM$TimeAfterRemoval:GLM$TreatmentPredator -0.1791 0.8399 -0.213 0.831
GLM$TimePreIntro:GLM$TreatmentPredator 1.7496 1.1496 1.522 0.128
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

Null deviance: 1720.2 on 270 degrees of freedom
Residual deviance: 258.3 on 261 degrees of freedom
AIC: 378.23

Number of Fisher Scoring iterations: 6


Leif K. Rasmuson

Doctoral Candidate
Oregon Institute of Marine Biology
Phone: (253)961-1763
E-Mail: Rasmuson at uoregon.edu

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